Fitting waggle dance models to waggle dance data

This document contains code to fit the waggle dance model to each of our 20 different sites. The code here uses the wagglefit package, as well as some additional code stored in fit_data.R to help simplify things. Each site has its own section, with reused code. The final sections create map plots and summary statistic plots.

Optimising each site

# set waggle dance duration in seconds as foraging distance for analysis
data <- read.csv("data/FullHBForagingData.csv")

alldata <- data %>%
  filter(Year == 2017) %>% # remove pilot data conducted in 2016
  select(date, site, duration.seconds) %>%
  rename(foraging_distance = duration.seconds)

BEL

Provides a good fit on the data. All parameters look central and nicely covered.

target_site <- "BEL"

# subset data for target site
data <- alldata %>%
  filter(site == target_site)

# set up bounds for the collective model
p_bnds <- c(0, 1.0)
bs_bnds <- c(1.0e-6, 10)
br_bnds <- c(1.0e-6, 10)
as_bnds <- c(1.0e-12, 1.5)
ar_bnds <- c(1.0e-12, 1.5)
collective_bounds <- rbind(
  p_bnds, bs_bnds,
  br_bnds, as_bnds,
  ar_bnds
)

# set up bounds for the individual model
bs_bnds <- c(1.0e-6, 10)
as_bnds <- c(1.0e-12, 0.1)
individual_bounds <- rbind(
  bs_bnds, as_bnds
)

# set coordinates for histogram subplot
subplot_coords <- c(0.1, 8, -5.5, -1.8)

all_sites[[target_site]] <- run_wagglefit_analysis(
  target_site, data, collective_bounds, individual_bounds, subplot_coords
)

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all_sites[[target_site]]$fit_result %>%
  kbl() %>%
  kable_classic(full_width = F)

site	model	loglikelihood	p	bs	br	as	ar	k	AIC	ks_statistic	ks_pvalue
BEL	collective	-181.4148	0.6475794	7.041855	0.8144974	0.0514862	0.1698127	5	372.8296	0.0980392	0.686
BEL	individual	-183.5011	1.0000000	4.495285	NA	0.0725148	NA	2	371.0021	0.0882353	0.770

all_sites[[target_site]]$fit

BFI

All parameters look central in the likelihood space and a nice fit is returned.

target_site <- "BFI"

# subset data for target site
data <- alldata %>%
  filter(site == target_site)

# set up bounds for the collective model
p_bnds <- c(0, 1.0)
bs_bnds <- c(1.0e-6, 10)
br_bnds <- c(1.0e-6, 10)
as_bnds <- c(1.0e-12, 1.5)
ar_bnds <- c(1.0e-12, 0.5)
bounds <- rbind(
  p_bnds, bs_bnds,
  br_bnds, as_bnds,
  ar_bnds
)

# set up bounds for the individual model
bs_bnds <- c(1.0e-6, 10)
as_bnds <- c(1.0e-12, 0.6)
bounds <- rbind(
  bs_bnds, as_bnds
)

# set coordinates for histogram subplot
subplot_coords <- c(0.2, 3.5, -6.5, -2.)

all_sites[[target_site]] <- run_wagglefit_analysis(
  target_site, data, collective_bounds, individual_bounds, subplot_coords
)

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all_sites[[target_site]]$fit_result %>%
  kbl() %>%
  kable_classic(full_width = F)

site	model	loglikelihood	p	bs	br	as	ar	k	AIC	ks_statistic	ks_pvalue
BFI	collective	-190.4988	0.0445303	0.000001	2.792133	0.1642228	0.2480057	5	390.9975	0.0873362	0.319
BFI	individual	-211.2967	1.0000000	9.470271	NA	0.1000000	NA	2	426.5934	0.1834061	0.000

all_sites[[target_site]]$fit

BLO

The individual fit isnt great and the Bs paramater is increasing up to the boundry, indicating it can only really take on a straight line / exponential fit. The parameters for the collective model are fairly central in the likelihood space, the fit looks very good.

target_site <- "BLO"

# subset data for target site
data <- alldata %>%
  filter(site == target_site)

# set up bounds for the collective model
p_bnds <- c(0, 1.0)
bs_bnds <- c(1.0e-10, 5)
br_bnds <- c(1.0e-10, 5)
as_bnds <- c(1.0e-5, 5)
ar_bnds <- c(1.0e-10, 1.5)
collective_bounds <- rbind(
  p_bnds, bs_bnds,
  br_bnds, as_bnds,
  ar_bnds
)

# set up bounds for the individual model
bs_bnds <- c(1.0e-6, 5505)
as_bnds <- c(1.0e-12, 0.1)
individual_bounds <- rbind(
  bs_bnds, as_bnds
)

# set coordinates for histogram subplot
subplot_coords <- c(0.2, 9.5, -8., -2.2)

all_sites[[target_site]] <- run_wagglefit_analysis(
  target_site, data, collective_bounds, individual_bounds, subplot_coords
)

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all_sites[[target_site]]$fit_result %>%
  kbl() %>%
  kable_classic(full_width = F)

site	model	loglikelihood	p	bs	br	as	ar	k	AIC	ks_statistic	ks_pvalue
BLO	collective	-221.0260	0.2085372	1.785832	0.5709989	0.0677377	0.3591282	5	452.0519	0.0705882	0.766
BLO	individual	-237.3888	1.0000000	5504.999990	NA	0.0001222	NA	2	478.7776	0.1117647	0.205

all_sites[[target_site]]$fit

BUR

Bs and Br go in oposite directions. E.g. Bs approaches 0 whilst Br approaches an every higher number.

Fit looks good.

target_site <- "BUR"

# subset data for target site
data <- alldata %>%
  filter(site == target_site)

# set up bounds for the collective model
p_bnds <- c(0, 1.0)
bs_bnds <- c(1.0e-6, 500)
br_bnds <- c(1.0e-6, 500)
as_bnds <- c(1.0e-12, 1.5)
ar_bnds <- c(1.0e-12, 1.5)
collective_bounds <- rbind(
  p_bnds, bs_bnds,
  br_bnds, as_bnds,
  ar_bnds
)

# set up bounds for the individual model
bs_bnds <- c(1.0e-6, 10)
as_bnds <- c(1.0e-12, 0.1)
individual_bounds <- rbind(
  bs_bnds, as_bnds
)

# set coordinates for histogram subplot
subplot_coords <- c(0.1, 4, -6.8, -2.5)

all_sites[[target_site]] <- run_wagglefit_analysis(
  target_site, data, collective_bounds, individual_bounds, subplot_coords,
  xlims = c(0, 6)
)

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all_sites[[target_site]]$fit_result %>%
  kbl() %>%
  kable_classic(full_width = F)

site	model	loglikelihood	p	bs	br	as	ar	k	AIC	ks_statistic	ks_pvalue
BUR	collective	-118.3050	0.1117918	1e-06	500	0.1513287	0.0275375	5	246.6100	0.0670732	0.839
BUR	individual	-143.7177	1.0000000	1e+01	NA	0.1000000	NA	2	291.4355	0.1768293	0.007

all_sites[[target_site]]$fit

CAD

The collective model roughly follows the individual model but is able to acheive a slightly improved fit to the shoulder, hence it provides a higher likelihood score. The AIC indicates this is overfitting, suggesting the individual model provides a more parsimonious explanation.

\(p\) does not approach 1 as one might expect, indicating there is overfitting and so a comparison with an individual model is required.

target_site <- "CAD"

# subset data for target site
data <- alldata %>%
  filter(site == target_site)

# set up bounds for the collective model
p_bnds <- c(0, 1.0)
bs_bnds <- c(1.0e-6, 10)
br_bnds <- c(1.0e-6, 10)
as_bnds <- c(1.0e-12, 1.5)
ar_bnds <- c(1.0e-12, 1.5)
collective_bounds <- rbind(
  p_bnds, bs_bnds,
  br_bnds, as_bnds,
  ar_bnds
)

# set up bounds for the individual model
bs_bnds <- c(1.0e-6, 2)
as_bnds <- c(1.0e-12, 0.8)
individual_bounds <- rbind(
  bs_bnds, as_bnds
)

# set coordinates for histogram subplot
subplot_coords <- c(0.1, 1.8, -6, -1.2)

all_sites[[target_site]] <- run_wagglefit_analysis(
  target_site, data, collective_bounds, individual_bounds, subplot_coords
)

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all_sites[[target_site]]$fit_result %>%
  kbl() %>%
  kable_classic(full_width = F)

site	model	loglikelihood	p	bs	br	as	ar	k	AIC	ks_statistic	ks_pvalue
CAD	collective	-48.27826	0.1648534	1e-06	0.4278111	1.457025	0.3857796	5	106.5565	0.0821918	0.964
CAD	individual	-49.95312	1.0000000	1e-06	NA	0.385471	NA	2	103.9062	0.1095890	0.734

all_sites[[target_site]]$fit

GIL

The collective model provides the most parsimonious and best fit.

target_site <- "GIL"

# subset data for target site
data <- alldata %>%
  filter(site == target_site)

# set up bounds for the collective model
p_bnds <- c(0, 1.0)
bs_bnds <- c(1.0e-6, 10)
br_bnds <- c(1.0e-6, 10)
as_bnds <- c(1.0e-12, 1.5)
ar_bnds <- c(1.0e-12, 1.5)
collective_bounds <- rbind(
  p_bnds, bs_bnds,
  br_bnds, as_bnds,
  ar_bnds
)

# set up bounds for the individual model
bs_bnds <- c(1.0e-6, 10)
as_bnds <- c(1.0e-12, 0.8)
individual_bounds <- rbind(
  bs_bnds, as_bnds
)

# set coordinates for histogram subplot
subplot_coords <- c(0.1, 2.1, -8., -2)

all_sites[[target_site]] <- run_wagglefit_analysis(
  target_site, data, collective_bounds, individual_bounds, subplot_coords
)

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all_sites[[target_site]]$fit_result %>%
  kbl() %>%
  kable_classic(full_width = F)

site	model	loglikelihood	p	bs	br	as	ar	k	AIC	ks_statistic	ks_pvalue
GIL	collective	-74.54118	0.2602914	0.000001	1e-06	0.3345677	0.7541017	5	159.0824	0.1302083	0.062
GIL	individual	-102.30919	1.0000000	2.036505	NA	0.3450190	NA	2	208.6184	0.1979167	0.001

all_sites[[target_site]]$fit

HER

The collective model provides the best fit to the data, but the proportion of scouts is high.

target_site <- "HER"

# subset data for target site
data <- alldata %>%
  filter(site == target_site)

# set up bounds for the collective model
p_bnds <- c(0, 1.0)
bs_bnds <- c(1.0e-6, 100)
br_bnds <- c(1.0e-6, 100)
as_bnds <- c(1.0e-12, 1.5)
ar_bnds <- c(1.0e-12, 1.5)
collective_bounds <- rbind(
  p_bnds, bs_bnds,
  br_bnds, as_bnds,
  ar_bnds
)

# set up bounds for the individual model
bs_bnds <- c(1.0e-6, 10)
as_bnds <- c(1.0e-12, 2)
individual_bounds <- rbind(
  bs_bnds, as_bnds
)

# set coordinates for histogram subplot
subplot_coords <- c(0.1, 4, -6.5, -1.5)

all_sites[[target_site]] <- run_wagglefit_analysis(
  target_site, data, collective_bounds, individual_bounds, subplot_coords
)

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all_sites[[target_site]]$fit_result %>%
  kbl() %>%
  kable_classic(full_width = F)

site	model	loglikelihood	p	bs	br	as	ar	k	AIC	ks_statistic	ks_pvalue
HER	collective	-136.9744	0.2647597	1e-06	0.1951346	0.3925715	0.1818652	5	283.9487	0.0786517	0.946
HER	individual	-138.9302	1.0000000	1e-06	NA	0.1751023	NA	2	281.8604	0.1123596	0.602

all_sites[[target_site]]$fit

HHS

Collective model provides the best fit but falls under the tail and shoulder. The individual model strugles to find a good fit, probably due to the tail.

target_site <- "HHS"

# subset data for target site
data <- alldata %>%
  filter(site == target_site)

# set up bounds for the collective model
p_bnds <- c(0, 1.0)
bs_bnds <- c(1.0e-6, 50)
br_bnds <- c(1.0e-6, 50)
as_bnds <- c(1.0e-12, 1.5)
ar_bnds <- c(1.0e-12, 1.5)
collective_bounds <- rbind(
  p_bnds, bs_bnds,
  br_bnds, as_bnds,
  ar_bnds
)

# set up bounds for the individual model
bs_bnds <- c(1.0e-6, 10)
as_bnds <- c(1.0e-12, 1.1)
individual_bounds <- rbind(
  bs_bnds, as_bnds
)

# set coordinates for histogram subplot
subplot_coords <- c(0.1, 4, -6.5, -2.2)

all_sites[[target_site]] <- run_wagglefit_analysis(
  target_site, data, collective_bounds, individual_bounds, subplot_coords
)

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all_sites[[target_site]]$fit_result %>%
  kbl() %>%
  kable_classic(full_width = F)

site	model	loglikelihood	p	bs	br	as	ar	k	AIC	ks_statistic	ks_pvalue
HHS	collective	-61.34801	0.0958427	0.000001	1e-06	0.1411094	0.5030629	5	132.6960	0.1333333	0.378
HHS	individual	-83.74915	1.0000000	7.095172	NA	0.1251512	NA	2	171.4983	0.2444444	0.008

all_sites[[target_site]]$fit

HOR

Collective model provides a very good fit, whilst the individual model fails to find much traction. The proportion of scouts goes very low (~3%) suggesting the majority of the colony are following a small number of scouting individuals.

target_site <- "HOR"

# subset data for target site
data <- alldata %>%
  filter(site == target_site)

# set up bounds for the collective model
p_bnds <- c(0, 1.0)
bs_bnds <- c(1.0e-6, 10)
br_bnds <- c(1.0e-6, 10)
as_bnds <- c(1.0e-12, 1.5)
ar_bnds <- c(1.0e-12, 1.5)
collective_bounds <- rbind(
  p_bnds, bs_bnds,
  br_bnds, as_bnds,
  ar_bnds
)

# set up bounds for the individual model
bs_bnds <- c(1.0e-6, 10)
as_bnds <- c(1.0e-12, 1.1)
individual_bounds <- rbind(
  bs_bnds, as_bnds
)

# set coordinates for histogram subplot
subplot_coords <- c(0.1, 3, -9, -2.5)

all_sites[[target_site]] <- run_wagglefit_analysis(
  target_site, data, collective_bounds, individual_bounds, subplot_coords
)

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all_sites[[target_site]]$fit_result %>%
  kbl() %>%
  kable_classic(full_width = F)

site	model	loglikelihood	p	bs	br	as	ar	k	AIC	ks_statistic	ks_pvalue
HOR	collective	-40.50196	0.0557362	0.000001	0.5398227	0.2184255	0.6281351	5	91.00393	0.0533333	0.968
HOR	individual	-56.65192	1.0000000	7.774875	NA	0.2019358	NA	2	117.30385	0.1666667	0.032

all_sites[[target_site]]$fit

MAK

Again the collective model provides a good fit to the data, however, the individual model fits poorly, reducing to an exponential.

target_site <- "MAK"

# subset data for target site
data <- alldata %>%
  filter(site == target_site)

# set up bounds for the collective model
p_bnds <- c(0, 1.0)
bs_bnds <- c(1.0e-6, 10)
br_bnds <- c(1.0e-6, 10)
as_bnds <- c(1.0e-12, 1.5)
ar_bnds <- c(1.0e-12, 0.5)
collective_bounds <- rbind(
  p_bnds, bs_bnds,
  br_bnds, as_bnds,
  ar_bnds
)

# set up bounds for the individual model
bs_bnds <- c(1.0e-6, 20)
as_bnds <- c(1.0e-12, 1.1)
individual_bounds <- rbind(
  bs_bnds, as_bnds
)

# run individual model
individual_result <- fit_individual_model_to_data(data, bounds)

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# view individual model likelihood space to check bounds look ok
individual_result$llspace

# set coordinates for histogram subplot
subplot_coords <- c(0.1, 4.2, -6.5, -2.5)

all_sites[[target_site]] <- run_wagglefit_analysis(
  target_site, data, collective_bounds, individual_bounds, subplot_coords
)

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#> [1] "Itteration 3"
#> [1] "Itteration 4"
#> [1] "Itteration 5"
#> [1] "Itteration 6"
#> [1] "Itteration 7"
#> [1] "Itteration 8"
#> [1] "Itteration 9"
#> [1] "Itteration 10"
#> [1] "Itteration 1"
#> [1] "Itteration 2"
#> [1] "Itteration 3"
#> [1] "Itteration 4"
#> [1] "Itteration 5"
#> [1] "Itteration 6"
#> [1] "Itteration 7"
#> [1] "Itteration 8"
#> [1] "Itteration 9"
#> [1] "Itteration 10"

all_sites[[target_site]]$fit_result %>%
  kbl() %>%
  kable_classic(full_width = F)

site	model	loglikelihood	p	bs	br	as	ar	k	AIC	ks_statistic	ks_pvalue
MAK	collective	-84.51875	0.2093455	2.319365	0.0201563	0.1221729	0.4776196	5	179.0375	0.0909091	0.789
MAK	individual	-98.02457	1.0000000	9.168368	NA	0.0961027	NA	2	200.0491	0.1919192	0.049

all_sites[[target_site]]$fit

MEL

Collective model provides the best fit, however it misses a large section of the shoulder for the tail. The \(bs\) parameter wants to go to zero, however when let go bellow 1e-6 the behaviour becomes very erratic and the fit deteriorates.

target_site <- "MEL"

# subset data for target site
data <- alldata %>%
  filter(site == target_site)

# set up bounds for the collective model
p_bnds <- c(0, 1.0)
bs_bnds <- c(1.0e-6, 10)
br_bnds <- c(1.0e-6, 10)
as_bnds <- c(1.0e-12, 1.5)
ar_bnds <- c(1.0e-12, 0.5)
collective_bounds <- rbind(
  p_bnds, bs_bnds,
  br_bnds, as_bnds,
  ar_bnds
)

# set up bounds for the individual model
bs_bnds <- c(1.0e-6, 10)
as_bnds <- c(1.0e-12, 1.1)
individual_bounds <- rbind(
  bs_bnds, as_bnds
)

# set coordinates for histogram subplot
subplot_coords <- c(0.1, 3., -7, -2.1)

all_sites[[target_site]] <- run_wagglefit_analysis(
  target_site, data, collective_bounds, individual_bounds, subplot_coords
)

#> [1] "Itteration 1"
#> [1] "Itteration 2"
#> [1] "Itteration 3"
#> [1] "Itteration 4"
#> [1] "Itteration 5"
#> [1] "Itteration 6"
#> [1] "Itteration 7"
#> [1] "Itteration 8"
#> [1] "Itteration 9"
#> [1] "Itteration 10"
#> [1] "Itteration 1"
#> [1] "Itteration 2"
#> [1] "Itteration 3"
#> [1] "Itteration 4"
#> [1] "Itteration 5"
#> [1] "Itteration 6"
#> [1] "Itteration 7"
#> [1] "Itteration 8"
#> [1] "Itteration 9"
#> [1] "Itteration 10"

all_sites[[target_site]]$fit_result %>%
  kbl() %>%
  kable_classic(full_width = F)

site	model	loglikelihood	p	bs	br	as	ar	k	AIC	ks_statistic	ks_pvalue
MEL	collective	-115.3163	0.0803693	1e-06	1.4e-06	0.2131210	0.3377032	5	240.6327	0.1626016	0.076
MEL	individual	-135.7308	1.0000000	1e-06	NA	0.2520821	NA	2	275.4617	0.2439024	0.002

all_sites[[target_site]]$fit

MPA

Collective provides the best fit.

target_site <- "MPA"

# subset data for target site
data <- alldata %>%
  filter(site == target_site)

# set up bounds for the collective model
p_bnds <- c(0, 1.0)
bs_bnds <- c(1.0e-6, 10)
br_bnds <- c(1.0e-6, 10)
as_bnds <- c(1.0e-12, 1.5)
ar_bnds <- c(1.0e-12, 0.5)
collective_bounds <- rbind(
  p_bnds, bs_bnds,
  br_bnds, as_bnds,
  ar_bnds
)

# set up bounds for the individual model
bs_bnds <- c(1.0e-6, 10)
as_bnds <- c(1.0e-12, 1.1)
individual_bounds <- rbind(
  bs_bnds, as_bnds
)

# set coordinates for histogram subplot
subplot_coords <- c(0.1, 4., -7.2, -2.1)

all_sites[[target_site]] <- run_wagglefit_analysis(
  target_site, data, collective_bounds, individual_bounds, subplot_coords
)

#> [1] "Itteration 1"
#> [1] "Itteration 2"
#> [1] "Itteration 3"
#> [1] "Itteration 4"
#> [1] "Itteration 5"
#> [1] "Itteration 6"
#> [1] "Itteration 7"
#> [1] "Itteration 8"
#> [1] "Itteration 9"
#> [1] "Itteration 10"
#> [1] "Itteration 1"
#> [1] "Itteration 2"
#> [1] "Itteration 3"
#> [1] "Itteration 4"
#> [1] "Itteration 5"
#> [1] "Itteration 6"
#> [1] "Itteration 7"
#> [1] "Itteration 8"
#> [1] "Itteration 9"
#> [1] "Itteration 10"

all_sites[[target_site]]$fit_result %>%
  kbl() %>%
  kable_classic(full_width = F)

site	model	loglikelihood	p	bs	br	as	ar	k	AIC	ks_statistic	ks_pvalue
MPA	collective	-181.8729	0.5669538	0.5783212	1e-06	0.1853653	0.419991	5	373.7458	0.0666667	0.880
MPA	individual	-188.0378	1.0000000	1.4738536	NA	0.1866656	NA	2	380.0756	0.1000000	0.404

all_sites[[target_site]]$fit

ROT

Colletive provides the best fit.

target_site <- "ROT"

# subset data for target site
data <- alldata %>%
  filter(site == target_site)

# set up bounds for the collective model
p_bnds <- c(0, 1.0)
bs_bnds <- c(1.0e-6, 10)
br_bnds <- c(1.0e-6, 10)
as_bnds <- c(1.0e-12, 1.5)
ar_bnds <- c(1.0e-12, 0.5)
collective_bounds <- rbind(
  p_bnds, bs_bnds,
  br_bnds, as_bnds,
  ar_bnds
)

# set up bounds for the individual model
bs_bnds <- c(1.0e-6, 10)
as_bnds <- c(1.0e-12, 1.1)
individual_bounds <- rbind(
  bs_bnds, as_bnds
)

# set coordinates for histogram subplot
subplot_coords <- c(0.1, 2., -5.5, -2.1)

all_sites[[target_site]] <- run_wagglefit_analysis(
  target_site, data, collective_bounds, individual_bounds, subplot_coords
)

#> [1] "Itteration 1"
#> [1] "Itteration 2"
#> [1] "Itteration 3"
#> [1] "Itteration 4"
#> [1] "Itteration 5"
#> [1] "Itteration 6"
#> [1] "Itteration 7"
#> [1] "Itteration 8"
#> [1] "Itteration 9"
#> [1] "Itteration 10"
#> [1] "Itteration 1"
#> [1] "Itteration 2"
#> [1] "Itteration 3"
#> [1] "Itteration 4"
#> [1] "Itteration 5"
#> [1] "Itteration 6"
#> [1] "Itteration 7"
#> [1] "Itteration 8"
#> [1] "Itteration 9"
#> [1] "Itteration 10"

all_sites[[target_site]]$fit_result %>%
  kbl() %>%
  kable_classic(full_width = F)

site	model	loglikelihood	p	bs	br	as	ar	k	AIC	ks_statistic	ks_pvalue
ROT	collective	-138.1292	0.3075642	1e-06	1e-06	0.3144194	0.4828687	5	286.2584	0.1494845	0.022
ROT	individual	-153.3550	1.0000000	1e-06	NA	0.3537984	NA	2	310.7100	0.2010309	0.000

all_sites[[target_site]]$fit

SAU

Collective provides the best fit.

target_site <- "SAU"

# subset data for target site
data <- alldata %>%
  filter(site == target_site)

# set up bounds for the collective model
p_bnds <- c(0, 1.0)
bs_bnds <- c(1.0e-6, 10)
br_bnds <- c(1.0e-6, 10)
as_bnds <- c(1.0e-12, 1.5)
ar_bnds <- c(1.0e-12, 0.5)
collective_bounds <- rbind(
  p_bnds, bs_bnds,
  br_bnds, as_bnds,
  ar_bnds
)

# set up bounds for the individual model
bs_bnds <- c(1.0e-6, 10)
as_bnds <- c(1.0e-12, 1.1)
individual_bounds <- rbind(
  bs_bnds, as_bnds
)

# set coordinates for histogram subplot
subplot_coords <- c(0.1, 2.5, -6.5, -2.1)

all_sites[[target_site]] <- run_wagglefit_analysis(
  target_site, data, collective_bounds, individual_bounds, subplot_coords
)

#> [1] "Itteration 1"
#> [1] "Itteration 2"
#> [1] "Itteration 3"
#> [1] "Itteration 4"
#> [1] "Itteration 5"
#> [1] "Itteration 6"
#> [1] "Itteration 7"
#> [1] "Itteration 8"
#> [1] "Itteration 9"
#> [1] "Itteration 10"
#> [1] "Itteration 1"
#> [1] "Itteration 2"
#> [1] "Itteration 3"
#> [1] "Itteration 4"
#> [1] "Itteration 5"
#> [1] "Itteration 6"
#> [1] "Itteration 7"
#> [1] "Itteration 8"
#> [1] "Itteration 9"
#> [1] "Itteration 10"

all_sites[[target_site]]$fit_result %>%
  kbl() %>%
  kable_classic(full_width = F)

site	model	loglikelihood	p	bs	br	as	ar	k	AIC	ks_statistic	ks_pvalue
SAU	collective	-108.1850	0.3106744	0.000001	9.989483	0.2625077	0.1638698	5	226.3701	0.0606061	0.956
SAU	individual	-115.5025	1.0000000	1.488528	NA	0.2710389	NA	2	235.0051	0.1287879	0.195

all_sites[[target_site]]$fit

SOM

Collective provides the best fit but misses a large section of the shoulder.

target_site <- "SOM"

# subset data for target site
data <- alldata %>%
  filter(site == target_site) %>%
  filter(foraging_distance < 6) # remove outlier distance

# set up bounds for the collective model
p_bnds <- c(0, 1.0)
bs_bnds <- c(1.0e-6, 10)
br_bnds <- c(1.0e-6, 10)
as_bnds <- c(1.0e-12, 1.5)
ar_bnds <- c(1.0e-12, 0.5)
collective_bounds <- rbind(
  p_bnds, bs_bnds,
  br_bnds, as_bnds,
  ar_bnds
)

# set up bounds for the individual model
bs_bnds <- c(1.0e-6, 10)
as_bnds <- c(1.0e-12, 1.1)
individual_bounds <- rbind(
  bs_bnds, as_bnds
)

# set coordinates for histogram subplot
subplot_coords <- c(0.1, 2., -5.5, -2.1)

all_sites[[target_site]] <- run_wagglefit_analysis(
  target_site, data, collective_bounds, individual_bounds, subplot_coords
)

#> [1] "Itteration 1"
#> [1] "Itteration 2"
#> [1] "Itteration 3"
#> [1] "Itteration 4"
#> [1] "Itteration 5"
#> [1] "Itteration 6"
#> [1] "Itteration 7"
#> [1] "Itteration 8"
#> [1] "Itteration 9"
#> [1] "Itteration 10"
#> [1] "Itteration 1"
#> [1] "Itteration 2"
#> [1] "Itteration 3"
#> [1] "Itteration 4"
#> [1] "Itteration 5"
#> [1] "Itteration 6"
#> [1] "Itteration 7"
#> [1] "Itteration 8"
#> [1] "Itteration 9"
#> [1] "Itteration 10"

all_sites[[target_site]]$fit_result %>%
  kbl() %>%
  kable_classic(full_width = F)

site	model	loglikelihood	p	bs	br	as	ar	k	AIC	ks_statistic	ks_pvalue
SOM	collective	-70.53597	0.0020792	1e+01	10	1.5000000	0.1486462	5	151.0719	0.1071429	0.502
SOM	individual	-76.67133	1.0000000	1e-06	NA	0.3771941	NA	2	157.3427	0.1607143	0.107

all_sites[[target_site]]$fit

SRA

Collective provides the best fit.

target_site <- "SRA"

# subset data for target site
data <- alldata %>%
  filter(site == target_site)

# set up bounds for the collective model
p_bnds <- c(0, 1.0)
bs_bnds <- c(1.0e-6, 10)
br_bnds <- c(1.0e-6, 10)
as_bnds <- c(1.0e-12, 1.5)
ar_bnds <- c(1.0e-12, 0.5)
collective_bounds <- rbind(
  p_bnds, bs_bnds,
  br_bnds, as_bnds,
  ar_bnds
)

# set up bounds for the individual model
bs_bnds <- c(1.0e-6, 10)
as_bnds <- c(1.0e-12, 1.1)
individual_bounds <- rbind(
  bs_bnds, as_bnds
)

# set coordinates for histogram subplot
subplot_coords <- c(0.1, 3., -7.5, -2.1)

all_sites[[target_site]] <- run_wagglefit_analysis(
  target_site, data, collective_bounds, individual_bounds, subplot_coords
)

#> [1] "Itteration 1"
#> [1] "Itteration 2"
#> [1] "Itteration 3"
#> [1] "Itteration 4"
#> [1] "Itteration 5"
#> [1] "Itteration 6"
#> [1] "Itteration 7"
#> [1] "Itteration 8"
#> [1] "Itteration 9"
#> [1] "Itteration 10"
#> [1] "Itteration 1"
#> [1] "Itteration 2"
#> [1] "Itteration 3"
#> [1] "Itteration 4"
#> [1] "Itteration 5"
#> [1] "Itteration 6"
#> [1] "Itteration 7"
#> [1] "Itteration 8"
#> [1] "Itteration 9"
#> [1] "Itteration 10"

all_sites[[target_site]]$fit_result %>%
  kbl() %>%
  kable_classic(full_width = F)

site	model	loglikelihood	p	bs	br	as	ar	k	AIC	ks_statistic	ks_pvalue
SRA	collective	-123.3688	0.2420154	0.000001	0.2059797	0.2131200	0.4924467	5	256.7375	0.0519481	0.976
SRA	individual	-138.1142	1.0000000	3.002015	NA	0.2133652	NA	2	280.2284	0.1428571	0.064

all_sites[[target_site]]$fit

STU

Individual provides the best fit. Again, the proportion of scouts does not move towards 1. I.e. the collective model fails to reduce to the individual in the MLE fit.

target_site <- "STU"

# subset data for target site
data <- alldata %>%
  filter(site == target_site)

# set up bounds for the collective model
p_bnds <- c(0, 1.0)
bs_bnds <- c(1.0e-6, 10)
br_bnds <- c(1.0e-6, 10)
as_bnds <- c(1.0e-12, 1.5)
ar_bnds <- c(1.0e-12, 0.5)
collective_bounds <- rbind(
  p_bnds, bs_bnds,
  br_bnds, as_bnds,
  ar_bnds
)

# set up bounds for the individual model
bs_bnds <- c(1.0e-6, 10)
as_bnds <- c(1.0e-12, 1.1)
individual_bounds <- rbind(
  bs_bnds, as_bnds
)

# set coordinates for histogram subplot
subplot_coords <- c(0.1, 4, -6.5, -1.5)

all_sites[[target_site]] <- run_wagglefit_analysis(
  target_site, data, collective_bounds, individual_bounds, subplot_coords
)

#> [1] "Itteration 1"
#> [1] "Itteration 2"
#> [1] "Itteration 3"
#> [1] "Itteration 4"
#> [1] "Itteration 5"
#> [1] "Itteration 6"
#> [1] "Itteration 7"
#> [1] "Itteration 8"
#> [1] "Itteration 9"
#> [1] "Itteration 10"
#> [1] "Itteration 1"
#> [1] "Itteration 2"
#> [1] "Itteration 3"
#> [1] "Itteration 4"
#> [1] "Itteration 5"
#> [1] "Itteration 6"
#> [1] "Itteration 7"
#> [1] "Itteration 8"
#> [1] "Itteration 9"
#> [1] "Itteration 10"

all_sites[[target_site]]$fit_result %>%
  kbl() %>%
  kable_classic(full_width = F)

site	model	loglikelihood	p	bs	br	as	ar	k	AIC	ks_statistic	ks_pvalue
STU	collective	-155.6990	0.3538099	0.000001	1.021807	0.5202437	0.1560936	5	321.3981	0.0454545	1.000
STU	individual	-156.5403	1.0000000	1.346564	NA	0.1612383	NA	2	317.0806	0.0545455	0.998

all_sites[[target_site]]$fit

SWP

Collective provides the best fit.

target_site <- "SWP"

# subset data for target site
data <- alldata %>%
  filter(site == target_site)

# set up bounds for the collective model
p_bnds <- c(0, 1.0)
bs_bnds <- c(1.0e-6, 15)
br_bnds <- c(1.0e-6, 15)
as_bnds <- c(1.0e-12, 1.5)
ar_bnds <- c(1.0e-12, 0.5)
collective_bounds <- rbind(
  p_bnds, bs_bnds,
  br_bnds, as_bnds,
  ar_bnds
)

# set up bounds for the individual model
bs_bnds <- c(1.0e-6, 10)
as_bnds <- c(1.0e-12, 1.1)
individual_bounds <- rbind(
  bs_bnds, as_bnds
)

# set coordinates for histogram subplot
subplot_coords <- c(0.1, 2., -6, -1.5)

all_sites[[target_site]] <- run_wagglefit_analysis(
  target_site, data, collective_bounds, individual_bounds, subplot_coords
)

#> [1] "Itteration 1"
#> [1] "Itteration 2"
#> [1] "Itteration 3"
#> [1] "Itteration 4"
#> [1] "Itteration 5"
#> [1] "Itteration 6"
#> [1] "Itteration 7"
#> [1] "Itteration 8"
#> [1] "Itteration 9"
#> [1] "Itteration 10"
#> [1] "Itteration 1"
#> [1] "Itteration 2"
#> [1] "Itteration 3"
#> [1] "Itteration 4"
#> [1] "Itteration 5"
#> [1] "Itteration 6"
#> [1] "Itteration 7"
#> [1] "Itteration 8"
#> [1] "Itteration 9"
#> [1] "Itteration 10"

all_sites[[target_site]]$fit_result %>%
  kbl() %>%
  kable_classic(full_width = F)

site	model	loglikelihood	p	bs	br	as	ar	k	AIC	ks_statistic	ks_pvalue
SWP	collective	-40.42382	0	0.1699517	1.274713	0.0765841	0.3841755	5	90.84765	0.1000000	0.708
SWP	individual	-46.44077	1	0.0000010	NA	0.4236502	NA	2	96.88153	0.1444444	0.294

all_sites[[target_site]]$fit

YAL

Collective provides the best fit.

target_site <- "YAL"

# subset data for target site
data <- alldata %>%
  filter(site == target_site)

# set up bounds for the collective model
p_bnds <- c(0, 1.0)
bs_bnds <- c(1.0e-6, 10)
br_bnds <- c(1.0e-6, 10)
as_bnds <- c(1.0e-12, 1.5)
ar_bnds <- c(1.0e-12, 0.5)
collective_bounds <- rbind(
  p_bnds, bs_bnds,
  br_bnds, as_bnds,
  ar_bnds
)

# set up bounds for the individual model
bs_bnds <- c(1.0e-6, 10)
as_bnds <- c(1.0e-12, 1.1)
individual_bounds <- rbind(
  bs_bnds, as_bnds
)

# set coordinates for histogram subplot
subplot_coords <- c(0.1, 4., -8, -2.)

all_sites[[target_site]] <- run_wagglefit_analysis(
  target_site, data, collective_bounds, individual_bounds, subplot_coords
)

#> [1] "Itteration 1"
#> [1] "Itteration 2"
#> [1] "Itteration 3"
#> [1] "Itteration 4"
#> [1] "Itteration 5"
#> [1] "Itteration 6"
#> [1] "Itteration 7"
#> [1] "Itteration 8"
#> [1] "Itteration 9"
#> [1] "Itteration 10"
#> [1] "Itteration 1"
#> [1] "Itteration 2"
#> [1] "Itteration 3"
#> [1] "Itteration 4"
#> [1] "Itteration 5"
#> [1] "Itteration 6"
#> [1] "Itteration 7"
#> [1] "Itteration 8"
#> [1] "Itteration 9"
#> [1] "Itteration 10"

all_sites[[target_site]]$fit_result %>%
  kbl() %>%
  kable_classic(full_width = F)

site	model	loglikelihood	p	bs	br	as	ar	k	AIC	ks_statistic	ks_pvalue
YAL	collective	-205.7602	0.0783189	0.0000010	0.2991773	0.1805637	0.2729442	5	421.5204	0.0439560	0.993
YAL	individual	-222.4328	1.0000000	0.2168114	NA	0.2128333	NA	2	448.8656	0.0989011	0.298

all_sites[[target_site]]$fit

ZSL

Collective provides the best fit.

target_site <- "ZSL"

# subset data for target site
data <- alldata %>%
  filter(site == target_site)

# set up bounds for the collective model
p_bnds <- c(0, 1.0)
bs_bnds <- c(1.0e-6, 10)
br_bnds <- c(1.0e-6, 10)
as_bnds <- c(1.0e-12, 1.5)
ar_bnds <- c(1.0e-12, 0.5)
collective_bounds <- rbind(
  p_bnds, bs_bnds,
  br_bnds, as_bnds,
  ar_bnds
)

# set up bounds for the individual model
bs_bnds <- c(1.0e-6, 50)
as_bnds <- c(1.0e-12, 1.3)
individual_bounds <- rbind(
  bs_bnds, as_bnds
)

# set coordinates for histogram subplot
subplot_coords <- c(0.1, 1.8, -8, -2)

all_sites[[target_site]] <- run_wagglefit_analysis(
  target_site, data, collective_bounds, individual_bounds, subplot_coords
)

#> [1] "Itteration 1"
#> [1] "Itteration 2"
#> [1] "Itteration 3"
#> [1] "Itteration 4"
#> [1] "Itteration 5"
#> [1] "Itteration 6"
#> [1] "Itteration 7"
#> [1] "Itteration 8"
#> [1] "Itteration 9"
#> [1] "Itteration 10"
#> [1] "Itteration 1"
#> [1] "Itteration 2"
#> [1] "Itteration 3"
#> [1] "Itteration 4"
#> [1] "Itteration 5"
#> [1] "Itteration 6"
#> [1] "Itteration 7"
#> [1] "Itteration 8"
#> [1] "Itteration 9"
#> [1] "Itteration 10"

all_sites[[target_site]]$fit_result %>%
  kbl() %>%
  kable_classic(full_width = F)

site	model	loglikelihood	p	bs	br	as	ar	k	AIC	ks_statistic	ks_pvalue
ZSL	collective	-109.9970	0.2557863	0.0000010	0.8052304	0.3877946	0.5	5	229.9940	0.0361991	0.998
ZSL	individual	-119.9481	1.0000000	0.3918134	NA	0.4194463	NA	2	243.8962	0.0950226	0.274

all_sites[[target_site]]$fit

Overall findings

# save the analysis results for all sites
# save(all_sites, file = "results/site_fit_results.Rdata")

# group all site results together
df <- map(all_sites, 1) %>%
  bind_rows()

# save results
# saveRDS(df, file = "results/site_fit_results.Rda")

# all_sites$BFI$fit <- all_sites$BFI$fit +
#   ylim(0, 6) +
#   scale_x_continuous(breaks = seq(0, 6, by = 2))

# AIC plot
aic_plot <- df %>%
  group_by(site) %>%
  slice(which.min(AIC)) %>%
  select(model) %>%
  group_by(model) %>%
  summarise(lowest_AIC = n()) %>%
  ggplot(aes(x = model, y = lowest_AIC)) +
  geom_bar(stat = "identity") +
  labs(x = "Model", y = "Count") +
  scale_y_continuous(breaks = seq(0, 20, by = 2)) +
  theme(
    text = element_text(size = 42)
  )

ggsave(
  plot = aic_plot,
  filename = "results/figures/AIC_plot.png",
  width = 90,
  height = 110,
  units = "mm",
  dpi = 300
)

# ks plot
ks_plot_dist <- df %>%
  ggplot(aes(x = ks_pvalue)) +
  geom_histogram(bins = 10, binwidth = 0.1, col = "white") +
  geom_vline(xintercept = 0.05, color = "red", linetype = "dashed") +
  scale_y_continuous(breaks = seq(0, 12, by = 2)) +
  labs(x = "KS P value") +
  facet_wrap(~model, nrow = 3) +
  theme(
    text = element_text(size = 42),
    strip.background = element_blank()
  )


ggsave(
  plot = ks_plot_dist,
  filename = "results/figures/sites_ks.png",
  width = 86,
  height = 180,
  units = "mm",
  dpi = 300
)

ggsave(
  plot = all_sites$STU$fit,
  filename = "results/figures/STU.png",
  width = 90,
  height = 110,
  units = "mm",
  dpi = 300
)

ggsave(
  plot = all_sites$BFI$fit,
  filename = "results/figures/BUR.png",
  width = 90,
  height = 110,
  units = "mm",
  dpi = 300
)

Map plots

Code to make the individual mal plots. These figures are created standalone but are combined in to facets manually in an image processor.

library(ggplot2)
library(ggrepel)
library(gridExtra)
library(ggsn)
library(sf)
library(rworldmap)
library(ggspatial)
library(rnaturalearth)
library(rnaturalearthdata)


full_data_path <- "data/FullHBForagingData.csv"
data_raw <- tibble(read.csv(full_data_path))

map_data <- data_raw %>%
  select(
    site, lat, lon
  ) %>%
  distinct()

map_data <- df %>%
  group_by(site) %>%
  slice(which.min(AIC)) %>%
  select(site, model) %>%
  left_join(map_data, on = "site") %>%
  mutate(col = ifelse(site %in% c("STU", "BUR"), "1", "0"))

locations <- st_as_sf(
  map_data,
  coords = c("lon", "lat"), crs = 4326
)

# Extract selected sites for figure
selected_sites <- filter(map_data, site %in% c("STU", "BUR")) %>%
  mutate(
    label = ifelse(site == "STU", "c", "d")
  )

points_area <- st_bbox(locations)

worldmap <- ne_countries(scale = "large", returnclass = "sf")

# london area
london <- st_read(
  "shapefiles/London_Ward.shp"
)

#> Reading layer `London_Ward' from data source 
#>   `/home/joe/Documents/phd/HoneybeeResearch/wagglefit/analysis/shapefiles/London_Ward.shp' 
#>   using driver `ESRI Shapefile'
#> Simple feature collection with 649 features and 0 fields
#> Geometry type: POLYGON
#> Dimension:     XY
#> Bounding box:  xmin: 503568.2 ymin: 155850.8 xmax: 561957.5 ymax: 200933.9
#> Projected CRS: OSGB 1936 / British National Grid

london <- st_transform(
  london,
  CRS("+proj=longlat +datum=WGS84 +no_defs +ellps=WGS84 +towgs84=0,0,0")
)

inset <- ggplot() +
  geom_sf(
    data = worldmap,
    fill = "grey90",
    color = "#4b4949d0"
  ) +
  geom_sf(
    data = london,
    fill = "#ced0cffc",
    lwd = 0
  ) +
  coord_sf(
    xlim = c(points_area[[1]] - 0.1, points_area[[3]] + 0.1),
    ylim = c(points_area[[2]] - 0.1, points_area[[4]] + 0.1)
  ) +
  geom_point(
    data = map_data,
    aes(x = lon, y = lat, shape = model, colour = model), size = 1.5
  ) +
  geom_text(
    data = selected_sites, aes(x = lon, y = lat, label = label),
    nudge_x = c(0, -0.07), nudge_y = c(0.05, 0.05), size = 8
  ) +
  geom_point(
    data = selected_sites, aes(x = lon, y = lat), size = 1.5, shape = 4
  ) +
  annotation_north_arrow(
    location = "tr", which_north = "true",
    style = north_arrow_fancy_orienteering,
    height = unit(15, "mm"),
    width = unit(15, "mm"),
    text_cex = 1.5
  ) +
  annotation_scale(
    location = "br",
    text_cex = 1.5
  ) +
  scale_shape_manual(values = c(1, 2)) +
  scale_colour_manual(values = c("black", "red")) +
  theme_nothing() +
  scale_x_continuous(expand = c(0, 0)) +
  scale_y_continuous(expand = c(0, 0)) +
  labs(x = NULL, y = NULL) +
  theme(
    panel.border = element_rect(color = "black", fill = NA, size = .5)
  )

inset

# make full plot
base <- ggplot(data = worldmap) +
  geom_sf(
    fill = "#c4cfc8",
    color = "#4b4949d0",
    lwd = 0.2
  ) +
  coord_sf(
    xlim = c(-11, 3),
    ylim = c(49.5, 60)
  ) +
  # geom_point(data = map_data, aes(x = lon, y = lat), size = 0.2) +
  geom_rect(
    aes(
      xmin = points_area$xmin[[1]] - 0.1, xmax = points_area$xmax[[1]] + 0.1,
      ymin = points_area$ymin[[1]] - 0.1, ymax = points_area$ymax[[1]] + 0.1
    ),
    fill = NA,
    colour = "black",
    size = .02
  ) +
  theme_nothing() +
  scale_x_continuous(expand = c(0, 0)) +
  scale_y_continuous(expand = c(0, 0)) +
  labs(x = NULL, y = NULL) +
  theme(
    panel.border = element_rect(color = "black", fill = NA, size = .5)
  )

base

merge_plot <- base +
  annotation_custom(
    ggplotGrob(inset),
    xmin = 1,
    xmax = 13,
    ymin = 52.5,
    ymax = 60
  )

merge_plot

ggsave(
  plot = merge_plot,
  filename = "results/figures/site_map.png",
  width = 90,
  height = 110,
  units = "mm",
  dpi = 300
)


merge_plot_2 <- inset +
  annotation_custom(
    ggplotGrob(base),
    xmin = -3.45,
    xmax = 2.2,
    ymin = 51.01,
    ymax = 51.45
  )

merge_plot_2

sites_model_plot <- plot_grid(
  merge_plot_2, ks_plot_dist, all_sites$STU$fit, all_sites$BUR$fit,
  labels = c("A", "B", "C", "D"), label_size = 24
)

ggsave(
  plot = sites_model_plot,
  filename = "results/figures/sites_model_plot.png",
  width = 183,
  height = 190,
  units = "mm",
  dpi = 300
)

ggsave(
  plot = sites_model_plot,
  filename = "results/figures/sites_model_plot.svg",
  width = 183,
  height = 190,
  units = "mm",
  dpi = 300
)

ggsave(
  plot = sites_model_plot,
  filename = "results/figures/sites_model_plot.pdf",
  width = 183,
  height = 190,
  units = "mm",
  dpi = 300
)

model_sites_fits <- plot_grid(
  merge_plot_2, ks_plot_dist,
  labels = c("A", "B"), label_size = 24
)

ggsave(
  plot = model_sites_fits,
  filename = "results/figures/model_sites_fits.png",
  width = 183,
  height = 190,
  units = "mm",
  dpi = 300
)

stu_zsl_fit <- plot_grid(
  all_sites$STU$fit, all_sites$BUR$fit,
  labels = c("A", "B"), label_size = 24
)

ggsave(
  plot = stu_zsl_fit,
  filename = "results/figures/stu_zsl_fit.svg",
  width = 183,
  height = 190,
  units = "mm",
  dpi = 100
)

# other map plots
inset <- ggplot() +
  geom_sf(
    data = worldmap,
    fill = "grey90",
    color = "#4b4949d0"
  ) +
  geom_sf(
    data = london,
    fill = "#ced0cffc",
    lwd = 0
  ) +
  coord_sf(
    xlim = c(points_area[[1]] - 0.1, points_area[[3]] + 0.1),
    ylim = c(points_area[[2]] - 0.1, points_area[[4]] + 0.1)
  ) +
  geom_point(
    data = map_data,
    aes(x = lon, y = lat, shape = model, colour = model), size = 1.5
  ) +
  annotation_north_arrow(
    location = "tr", which_north = "true",
    style = north_arrow_fancy_orienteering,
    height = unit(10, "mm"),
    width = unit(10, "mm")
  ) +
  annotation_scale(
    location = "br",
    text_cex = 3
  ) +
  scale_shape_manual(values = c(1, 2)) +
  scale_colour_manual(values = c("black", "red")) +
  theme_nothing() +
  scale_x_continuous(expand = c(0, 0)) +
  scale_y_continuous(expand = c(0, 0)) +
  labs(x = NULL, y = NULL) +
  theme(
    panel.border = element_rect(color = "black", fill = NA, size = .5),
    text = element_text(size = 42)
  )

inset

# make full plot
base <- ggplot(data = worldmap) +
  geom_sf(
    fill = "#c4cfc8",
    color = "#4b4949d0",
    lwd = 0.2
  ) +
  coord_sf(
    xlim = c(-11, 15),
    ylim = c(49.5, 60)
  ) +
  geom_point(data = map_data, aes(x = lon, y = lat), size = 0.2) +
  geom_rect(
    aes(
      xmin = points_area$xmin[[1]] - 0.1, xmax = points_area$xmax[[1]] + 0.1,
      ymin = points_area$ymin[[1]] - 0.1, ymax = points_area$ymax[[1]] + 0.1
    ),
    fill = NA,
    colour = "black",
    size = .02
  ) +
  theme_nothing() +
  scale_x_continuous(expand = c(0, 0)) +
  scale_y_continuous(expand = c(0, 0)) +
  labs(x = NULL, y = NULL) +
  theme(
    panel.border = element_rect(color = "black", fill = NA, size = .5)
  )

merge_plot <- base +
  annotation_custom(
    ggplotGrob(inset),
    xmin = 1,
    xmax = 13,
    ymin = 52.5,
    ymax = 60
  )

merge_plot

ggsave(
  plot = merge_plot,
  filename = "results/figures/site_map.png",
  width = 183,
  height = 190,
  units = "mm",
  dpi = 300
)


sites_model_plot <- plot_grid(
  all_sites$STU$fit, all_sites$BUR$fit, aic_plot, ks_plot_dist,
  labels = c("A", "B", "C", "D"), label_size = 42
)

sites_model_plot

ggsave(
  plot = sites_model_plot,
  filename = "results/figures/results_model_plot.png",
  width = 183,
  height = 190,
  units = "mm",
  dpi = 300
)